k-Inductive Invariant Checking for Graph Transformation Systems [chapter]

Johannes Dyck, Holger Giese
2017 Lecture Notes in Computer Science  
We prove the approach's correctness and demonstrate its applicability by means of several examples evaluated with a prototypical implementation of our algorithm. While our technique takes care of the inductive step (verifying the k-inductive invariant), the base of induction for traces of length k − 1 from an initial graph is established with the model checker GROOVE [9]. This report is organized as follows: In Section 2, we reintroduce the necessary foundations and our formal model. Section 3
more » ... efines our notion of k-inductive invariants and the symbolic encoding. We present our formal approach to k-inductive invariant checking in Section 4. In Section 5, we evaluate our algorithm and approach, before summarizing our results in Section 6. Omitted constructions and proofs can be found in the respective sources. More details to our examples can be found in Appendix A. This report is an extended version of [6] and provides proofs to our lemmas and theorems and additional details to our example systems and evaluation. The numbering of definitions, theorems, examples, and lemmas follows the numbering in [6] ; any such elements added in this report are not numbered. 8 2. Prerequisites Prerequisites This section cites formal foundations [7, 8, 10] , introduces our running example, and reintroduces the restricted formal model employed in our approach and tool.
doi:10.1007/978-3-319-61470-0_9 fatcat:jzlax4qgwvdfdpifrwkvlnvt3y